Question
When an object is in motion, its position changes with time. So, the quantity that describes how fast is the position changingm w.r.t. time and in what direction is given by average velocity. It is defined as the change in position or displacement $(\triangle\text{x})$ divided by the time interval $(\triangle\text{t})$ in which that displacement occur. However, the quantity used to describe the rate of motion over the actual path, is average speed. It defined as the total distance travelled by the object divided by the total time taken.

  1. A 250m long train is moving with a uniform velocity of 45kmh-1. The time taken by the train to cross a bridge of length 750m is:
  1. 56s
  2. 68s
  3. 80s
  4. 92s
  1. A truck requires 3hr to complete a journey of 150km. What is average speed?
  1. 50km/h
  2. 25km/h
  3. 15km/h
  4. 10km/h
  1. Average speed of a car between points A and B is 20m/s, between B andC is 15m/s and between C and D is 10m/s. What is the average speed between A and D, if the time taken in the mentioned sections is 20s, 10s and 5s, respectively?
  1. 17.14m/s
  2. 15m/s
  3. 10m/s
  4. 45m/s
  1. A cyclist is moving on a circular track of radius 40m completes half a revolution in 40s. Its average velocity is:
  1. $\text{Zero}$

  2. $2\text{ms}^{-1}$

  3. $4\pi\text{ms}^{-1}$

  4. $8\pi\text{ms}^{-1}$

  1. In the following graph, average velocity is geometrically represented by:

  1. Length of the line P1 P2.
  2. Slope of the straight line P1 P2.
  3. Slope of the tangent to the curve at P1.
  4. Slope of the tangent to the curve at P2.

Answer

  1. (c) 80s

Explanation:

Total time taken $=\frac{\text{Total distance}}{\text{Speed}}$

$\text{t}=\frac{250+750}{45\times\frac{5}{18}}=80\text{s}$

  1. (a) 50km/h

Explanation:

Average speed $=\frac{\text{Total distance}}{\text{Total time}}$

$=\frac{150}{3}=50\text{km}/\text{h}$

  1. (a) 17.14m/s

Explanation:

Total distance (d = tv)

= 20 × 20 + 15 × 10 + 10 × 5 = 600m

Total time = 20 + 10 + 5 = 35s

Therefore, average speed

 $=\frac{600}{35}=17.14\text{m}/\text{s}$

  1. (b) $2\text{ms}^{-1}$

Explanation:

Given, R = 40m and t = 40s

Average velocity $=\frac{\text{Total distance}}{\text{Time taken}}$

$=\frac{2\text{R}}{\text{t}}=\frac{2\times40}{40}=2\text{ms}^{-1}$

  1. (b) Slope of the straight line P1 P2.

Explanation:

From the position-time graph, average velocity is geometrically represented by the slope of curve, i.e. slope of straight line P1 P2.

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