**Motion Worksheet-5**

- A train travels at speed of 60 km/h for 0.52 h, at 30 km/h for the next 0.24 h and then at 70 km/h for the next 0.71 h. what is the average speed of the train in kmph? (approximately)

A. 60 B. 45 C. 50 D. 68

- A car travels a distance of 200 km from A to B towards North in 5 hours.

Calculate velocity of the car for this journey.

A. 45 km/h towards north B. 45 km/h towards south

C. 40 km/h towards north D. 40 km/h towards south

- A bus covers a distance of 250 km from A to B towards west in 5 hours in the morning and returns to A in the evening covering the same distance of 250 km in the same time of 5 hours. Find average velocity of the bus for the whole journey.

A. 50 km/h B. 40 km/h C. 0 km/h D. 45 km/h

- A driver decreases the speed of a car from 25 m/s in 5 seconds. Find the acceleration of the car.

A. 3 m/s^{2} B. -2 m/s^{2} C. -3 m/s^{2} D. 2 m/s^{2}

- A Particle is moving in a circular path of radius r. The displacement after half a circle would be :

A. 0 B. πr C. 2r D. 2πr

**Answer:**

- A

**Explanation: **In the problem, first of all we have to calculate the distance traveled by the train under three different conditions.

(i) In the first case, the train travels at a speed of 60 km/h for a time of 0.52 hours.

Now, Speed

So,

And, Distance

= 31.2 km …….(1)

(ii) In the second case, the train travels at a speed of 30 km/h for time of 0.24 hours.

So,

And, Distance = 30 × 0.24

= 7.2 km ……..(2)

(iii) In the third case, the train travels at a speed of 70 km/h for a time of 0.71 hours

So,

And, Distance = 70 × 0.71

= 49.7 km ………(3)

Now, from the equations (1), (2) and (3), we get :

Total distance travelled by train = 31.2 + 7.2 + 49.7

= 88.1 km ……….(4)

And, Total time taken = 0.52 + 0.24 + 0.71

= 1.47 h ………..(5)

Average speed =

= 88.1/1.47

= 59.9 k/h approx 60 kmph

- C

**Explanation:**

(i) Speed =

= 40 km/h

Thus, the speed (or average speed) of the car is 40 km/h.

(ii) Velocity =

= 40 km/h towards north

So, the velocity or average velocity of the car is 40 km/h towards north.

- C

**Explanation: **We have to be careful that average speed and average velocity of a body may be diferent. In this case;

(i) Average speed =

= 50 km/h

Thus, the average speed of the bus for the whole journey (both ways) is 50 kilometres per hour.

(ii) But to find out average velocity we have to calculate the displacement. Since the bus travels 250 km from A to B towards West and then comes back to starting point A in the reverse direction. So, the total displacement will be 250 km – 250 km = 0 km.

Now,

Average velocity =

= 0 km/h

Thus, the average velocity of the bus for the whole journey (both ways) is 0 kilometres per hour. No direction can be stated in this case of zero velocity.

- C

**Explanation: **In this problem the term ‘speed’ will be considered as ‘velocity’.

Here, Initial velocity of car, u = 25 m/s

Final velocity of car, v = 10 m/s

And, Time taken by the car t = 5 s

Now putting these values in the given formula for acceleration :

a = –3 m/s^{2}

Thus, the acceleration of car is, -3 m/s^{2}. The negative sign of acceleration means the speed of the car is going down that meand it is retardation. So, the car has a retardation of 3 m/s^{2}.

- C

**Explanation: **Displacement will be diameter (2 r) of the circle and distance travelled will be half of the circumference (πr) of the circle.