Motion Worksheet19

A train starting from rest moves with a uniform acceleration of 0.2 m/s^{2} for 5 minutes. Calculate the speed acquired and the distance travelled in this time.

Name the two quantities, the slope of whose graph gives:
(a) speed, and (b) acceleration

A deer starts from rest, and accelerates at 2 m/s^{2} for 10 seconds. Calculate :
(a) the final velocity
(b) the distance travelled.

A train travelling at 20 m/s^{–1} accelerates at 0.5 m/s^{2}for 30 s. How far will it travel in this time?

A cyclist is travelling at 15 m/s^{–1}. He applies brakes so that he does not collide with a wall 18 m away. What deceleration must he have?

Draw a velocitytime graph to show the following motion :
A car accelerates uniformly from rest for 5 s; then it travels at a steady velocity for 5 s.

The velocitytime graph for part of a train journey is a horizontal straight line. What does this tell you about (a) the train’s velocity, and (b) about its acceleration?

The graph gives alongside shows the positions of a body at different times. Calculate the speed of the body as it moves from :
(i) A to B
(ii) B to C, and
(iii) C to D.

What can you say about the motion of a body if:
(a) its displacementtime graph is a straight line?
(b) its velocitytime graph is a straight line?

A body with an initial velocity x moves with a uniform acceleration y. Plot its velocity–time graph.

Given here is the velocitytime graph for a cycle:
Find: (i) velocity of the cycle at point C.
(ii) Acceleration acting on the cycle between A and B.
(iii) Acceleration acting on the cycle between B and C.

A body is moving uniformly in a straight line with a velocity of 5 m/s. Find graphically the distance covered by it in 5 seconds.

The speedtime graph of an ascending passenger lift is given here.
What is the acceleration of the lift :
(i) during the first two seconds ?
(ii) between second and tenth second ?
(iii) during the last two second ?

A car is moving on a straight road with uniform acceleration. The speed of the car varies with time as follows :
Time (s) : 0 2 4 6 8 10
Speed(m/s) : 4 8 12 16 20 24
Draw the speedtime graph by choosing a convenient scale. From this graph :
(i) Calculate the acceleration of the car.
(ii) Calculate the distance travelled by the car in 10 seconds.

The graph given alongside shows how the speed of a car changes with time :
(i) What is the initial speed of the car?
(ii) What is the maximum speed attained by the car?
(iii) Which part of the graph shows zero acceleration?
(iv) Which part of the graph shows varying retardation?
(v) Find the distance travelled in first 8 hours?

A car is travelling along the road at 8 m/s^{–1}. It accelerates at 1 m/s^{–2} for a distance of 18 m. How fast is it then travelling?

A car is travelling at 20m/s along a road. A child runs out into the road 50 m ahead and the car driver steps on the brake pedal. What must the car’s deceleration be if the car is to stop just before it reaches the child?
Answer:

V = u + at & S = ut + ½ at^{2}
U = 0, v = ?
a = 0.2 m/s^{2}
t = 300 sec
v = 0 + .2 x 300 = 60 m/s
By putting the values in the second equation of motion the distance can be calculated.
S = 0 + ½ × 0.2 × 300 × 300 = 9000 m or 9 km

Distance time graph and Speedtime graph

20 m/s and 100 m

825 m

6. 25 m/s^{2}

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The train has uniform velocity and there is no acceleration.

(i) 3/3 = 1 cm/s, (ii) 0/2 = 0 cm/s, (iii) 2 m/s

Uniform velocity
Uniform acceleration

–

40 km/h, 6.6 km/h^{2}, 0

25 m

2.3 m/s^{2}, 0, –2.3 m/s^{2}

2 m/s^{2}, 140 m

10 km/h, 35 km/h, BC, CD, 242.5 km

10 m/s

4 m/s^{2}