Having speed $20\,\text{m/s}$, the car slows down and stops behind $8\,\text{s}$. Determine the acceleration modulus and the distance traveled.

a = 2{,}5\,\tfrac{\text{m}}{\text{s}^{2}}; S = 80\,\text{m}

The helicopter flew north $400\,\text{km}$, turned to $90^{\circ}$ and flew by $300\,\text{km}$ to the east. Find the path and the moving module.

\ell = 700\,\text{km}; S = 500\,\text{km}

A freight train left the station at a speed $60\,\text{km/ch}$. Half an hour later, an electric train left in the same direction at a speed $90\,\text{km/ch}$. How long after the train leaves and at what distance from the station will it catch up with the train?

t = 1{,}5\,\text{h}; S = 90\,\text{km}

The car slows down with acceleration $4\,\text{m/s}^{2}$ and stops behind $6\,\text{s}$. Determine the braking distance and initial speed. Did the driver violate the restriction? $90\,\text{km/ch}$?

S = 72\,\text{m}; v_0 = 24\,\tfrac{\text{m}}{\text{s}}; \text{did not violate}

A body falls freely from a height $125\,\text{m}$. After how long and at what speed will it fall to Earth? Accept $g=10\,\text{m/s}^{2}$.

t = 5\,\text{s}; v = 50\,\tfrac{\text{m}}{\text{s}}

A body is thrown upward with speed $30\,\text{m/s}$. How long will it take for it to be up? $40\,\text{m}$? Will it reach the heights $50\,\text{m}$?

t = 2\,\text{s}\ \text{or}\ 4\,\text{c}; \text{height }50\,\text{m not achieved}

A body is thrown from the Earth at an angle $60^{\circ}$ towards the horizon at speed $40\,\text{m/s}$. Determine the flight range and maximum lift height.

S = 138{,}6\,\text{m}; H = 60\,\text{m}

A body is thrown horizontally with a speed $15\,\text{m/s}$ and fell to Earth through $2\,\text{s}$. Determine the height, flight distance and speed when falling.

h = 20\,\text{m}; S = 30\,\text{m}; v = 25\,\tfrac{\text{m}}{\text{s}}

Body thrown with speed $30\,\text{m/s}$ at an angle to the horizontal. The maximum lift height is $26{,}5\,\text{m}$. Determine the throwing angle and flight distance.

\alpha = 50^{\circ}; S = 88{,}6\,\text{m}

The car moves around a bend with a radius $160\,\text{m}$. What is its speed if the centripetal acceleration is $2{,}5\,\text{m/s}^{2}$?

v = 20\,\tfrac{\text{m}}{\text{s}}

The body has an initial speed $10\,\text{m/s}$, then moves uniformly accelerated and for $5\,\text{s}$ passes $40\,\text{m}$. Determine the acceleration.

a = 0{,}8\,\tfrac{\text{m}}{\text{s}^{2}}

The runner moves in a circle with a radius $20\,\text{m}$. What are the path and the displacement module after $1{,}5$ circle?

\ell = 188{,}5\,\text{m}; S = 40\,\text{m}

The pedestrian passed $300\,\text{m}$ at speed $1{,}5\,\text{m/s}$, then again $2\,\text{min}$ moved at speed $2{,}5\,\text{m/s}$. Determine the average speed along the entire path.

v_{\text{av}} = 1{,}875\,\tfrac{\text{m}}{\text{s}}

Body thrown at an angle $60^{\circ}$ to the horizon and rose to a height $34\,\text{m}$. Determine the initial speed and flight range.

v_0 = 30\,\tfrac{\text{m}}{\text{s}}; S = 78\,\text{m}

A body is thrown horizontally from a height $20\,\text{m}$ and flew horizontally $30\,\text{m}$. Determine the speed when falling to Earth.

v = 25\,\tfrac{\text{m}}{\text{s}}

On the way $30\,\text{m}$ the car changed speed from $72\,\text{km/ch}$ up to $36\,\text{km/ch}$. Determine the acceleration.

a_x = -5\,\tfrac{\text{m}}{\text{s}^{2}}

In uniformly accelerated motion with acceleration $1{,}5\,\text{m/s}^{2}$ the body has passed $87\,\text{m}$ for $6\,\text{s}$. What is the initial speed?

v_0 = 10\,\tfrac{\text{m}}{\text{s}}

Body thrown at an angle $45^{\circ}$ towards the horizon, flew horizontally $22{,}5\,\text{m}$. Determine the initial speed and maximum altitude.

v_0 = 15\,\tfrac{\text{m}}{\text{s}}; H = 5{,}625\,\text{m}

A body is thrown horizontally and falls through $4\,\text{s}$, flying horizontally $120\,\text{m}$. Determine the height, initial horizontal velocity, and falling velocity.

h = 80\,\text{m}; v_{0x} = 30\,\tfrac{\text{m}}{\text{s}}; v = 50\,\tfrac{\text{m}}{\text{s}}

Body thrown at an angle $45^{\circ}$ to the horizon, fell to Earth through $5\,\text{s}$. Determine the initial speed, flight range and maximum altitude.

v_0 = 35{,}36\,\tfrac{\text{m}}{\text{s}}; S = 125\,\text{m}; H = 31{,}25\,\text{m}

10TH GRADE PRACTICE

Physics Problems: Kinematics, Grade 10

Description of linear and circular motion.

32 problems across 3 sub-topics

Practise in the interactive mode

Here the conditions and analysis of the solution can be read without an account. In the simulator, you need to collect the same analyzes yourself: “Given,” formulas, order of steps and answer.

Problem statements

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32 problems

Position in this set: 1 from 32

Problem #1

Kinematics: uniform motion

How long will it take the car to cover the distance? at speed ?

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Given

Find

Uniform motion: speed is the distance divided by the time.

Answer

Position in this set: 2 from 32

Problem #2

Kinematics: uniformly accelerated motion

Having speed , the car slows down and stops behind . Determine the acceleration modulus and the distance traveled.

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Given

Find

When braking to a stop, the acceleration module is equal to the initial speed divided by time.
The same path is given by writing through acceleration: S = at^2/2 = v_0^2/(2a).

Answer

Position in this set: 3 from 32

Problem #5

Kinematics: free fall and circular motion

Car wheel radius does it in a minute rpm Determine the period, frequency, angular velocity, linear velocity and centripetal acceleration of the extreme points. Then find the braking distance and acceleration modulus of the car if it stopped for .

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Given

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When moving equally slow to a stop, the average speed is half the initial speed.

Answer

Position in this set: 4 from 32

Problem #6

Kinematics: free fall and circular motion

A body is thrown vertically upward with a speed . How long will it take for it to return, what maximum height will it reach and what height will it be at in ?

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Given

Find

Ascent and descent take the same time, so t_2 = t_1.

Answer

Position in this set: 5 from 32

Problem #7

Kinematics: uniform motion

The helicopter flew north , turned to and flew by to the east. Find the path and the moving module.

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Given

Find

The path is the sum of the lengths of both sections.
The sections are perpendicular, so the displacement is the hypotenuse.

Answer

Position in this set: 6 from 32

Problem #8

Kinematics: uniform motion

A freight train left the station at a speed . Half an hour later, an electric train left in the same direction at a speed . How long after the train leaves and at what distance from the station will it catch up with the train?

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Given

Find

We count down time from the exit of the train.

Answer

Position in this set: 7 from 32

Problem #9

Kinematics: uniformly accelerated motion

The car slows down with acceleration and stops behind . Determine the braking distance and initial speed. Did the driver violate the restriction? ?

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Given

Find

Answer

Position in this set: 8 from 32

Problem #10

Kinematics: free fall and circular motion

Body thrown with speed . It is required to determine the movement for a throw from a height and from the surface of the Earth, but the direction of the initial velocity is not specified. Is there enough initial data for a definite answer?

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Position in this set: 9 from 32

Problem #11

Kinematics: free fall and circular motion

A body falls freely from a height . After how long and at what speed will it fall to Earth? Accept .

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Given

Find

The same result is given by the formula v = sqrt{2gh}.

Answer

Position in this set: 10 from 32

Problem #12

Kinematics: free fall and circular motion

A body is thrown upward with speed . How long will it take for it to be up? ? Will it reach the heights ?

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Given

Find

Two roots: the body passes this height on the ascent and on the descent.
The discriminant is negative, which means the body does not reach such a height.

Answer

Position in this set: 11 from 32

Problem #13

Kinematics: free fall and circular motion

A body is thrown from the Earth at an angle towards the horizon at speed . Determine the flight range and maximum lift height.

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Given

Find

Answer

Position in this set: 12 from 32

Problem #14

Kinematics: free fall and circular motion

Body thrown from a height at an angle towards the horizon at speed . At what speed will it fall to Earth?

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Position in this set: 13 from 32

Problem #15

Kinematics: free fall and circular motion

The balloon rises from the Earth with acceleration . Via a stone fell out of it. How long after separation and at what speed will the stone fall to Earth?

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Position in this set: 14 from 32

Problem #16

Kinematics: free fall and circular motion

A body is thrown horizontally with a speed and fell to Earth through . Determine the height, flight distance and speed when falling.

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Given

Find

With a horizontal throw, the initial vertical velocity is zero.

Answer

Position in this set: 15 from 32

Problem #17

Kinematics: free fall and circular motion

Body thrown with speed at an angle to the horizontal. The maximum lift height is . Determine the throwing angle and flight distance.

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Given

Find

Answer

Position in this set: 16 from 32

Problem #18

Kinematics: free fall and circular motion

The car is moving at speed . Wheel diameter . Determine the period, frequency, angular velocity and centripetal acceleration of the extreme points of the wheel. The car stops for : Find the braking distance and the number of revolutions during braking.

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Position in this set: 17 from 32

Problem #19

Kinematics: free fall and circular motion

From what height did the body fall if during the last second of the fall it flew: a) , b) ?

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Position in this set: 18 from 32

Problem #20

Kinematics: uniform motion

The tourist passed north, then some more in an unknown direction. Determine the path and possible range of the motion module.

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Position in this set: 19 from 32

Problem #21

Kinematics: uniform motion

Distance between piers . Current speed , speed of the boat relative to the water . How long will it take to get there and back?

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Given

Find

Velocities along the current are added, while against the current they are subtracted.

Answer

Position in this set: 20 from 32

Problem #22

Kinematics: free fall and circular motion

The car moves around a bend with a radius . What is its speed if the centripetal acceleration is ?

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Given

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Answer

Position in this set: 21 from 32

Problem #23

Kinematics: uniformly accelerated motion

The body has an initial speed , then moves uniformly accelerated and for passes . Determine the acceleration.

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Given

Find

Multiply by two to get rid of the fraction.
The minus sign means that the speed of the body decreases.

Answer

Position in this set: 22 from 32

Problem #24

Kinematics: free fall and circular motion

The runner moves in a circle with a radius . What are the path and the displacement module after circle?

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Given

Find

After one and a half laps, the runner finds himself at a diametrically opposite point.

Answer

Position in this set: 23 from 32

Problem #25

Kinematics: uniform motion

The pedestrian passed at speed , then again moved at speed . Determine the average speed along the entire path.

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Given

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Average speed is the entire path divided by the entire time, not the average of speeds.

Answer

Position in this set: 24 from 32

Problem #26

Kinematics: free fall and circular motion

Body thrown at an angle to the horizon and rose to a height . Determine the initial speed and flight range.

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Given

Find

The lifting height depends only on the vertical component of the speed.

Answer

Position in this set: 25 from 32

Problem #27

Kinematics: uniform motion

How far will the plane fly in , if its speed is ?

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Given

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Answer

Position in this set: 26 from 32

Problem #28

Kinematics: free fall and circular motion

A body is thrown horizontally from a height and flew horizontally . Determine the speed when falling to Earth.

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Given

Find

The initial vertical velocity during a horizontal throw is zero.

Answer

Position in this set: 27 from 32

Problem #29

Kinematics: uniformly accelerated motion

On the way the car changed speed from up to . Determine the acceleration.

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Given

Find

The formula without time connects speeds and paths directly.
The minus sign means braking; acceleration module is 5 m/s².

Answer

Position in this set: 28 from 32

Problem #30

Kinematics: uniformly accelerated motion

In uniformly accelerated motion with acceleration the body has passed for . What is the initial speed?

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Given

Find

The sign depends on whether the body is accelerating or decelerating.
Acceleration: acceleration is directed along the movement - this case is implied in the condition.
For comparison: this would be the case when braking with the same acceleration module.

Answer

Position in this set: 29 from 32

Problem #31

Kinematics: free fall and circular motion

Body thrown at an angle towards the horizon, flew horizontally . Determine the initial speed and maximum altitude.

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Given

Find

At an angle of 45°, the horizontal and vertical components are equal.

Answer

Position in this set: 30 from 32

Problem #32

Kinematics: free fall and circular motion

A body is thrown horizontally and falls through , flying horizontally . Determine the height, initial horizontal velocity, and falling velocity.

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Given

Find

Answer

Position in this set: 31 from 32

Problem #33

Kinematics: free fall and circular motion

Body thrown at an angle to the horizon, fell to Earth through . Determine the initial speed, flight range and maximum altitude.

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Given

Find

At 45° the components are equal.

Answer

Position in this set: 32 from 32

Problem #34

Kinematics: uniformly accelerated motion

The body has an initial speed and acceleration . How long will it take? ?

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Given

Find

We reduce to the usual quadratic equation for time.
We discard the negative root: time cannot be less than zero.

Answer

The theory behind these problems

Work through the topic if a problem will not give in.

Speed and uniform movementPath, time, speed, average speed and addition of movements.Uniformly accelerated motionAcceleration, speed and displacement under constant acceleration.Free fall and circular motionFall without resistance and kinematics of uniform rotation.

Formulas by topic

Look up symbols and units of measurement in the reference.

PeriodT · with Velocityv · m/s Angular velocityω · rad/s Accelerationa · m/s² Frequencyν · Hz