Question

The velocity-time (v-t) graph of a particle moving along a straight line is shown below. Find the average velocity of the particle in km/h.

Answer 1

Explanation:

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Answer 2

SOLUTION

GIVEN

The velocity-time (v-t) graph of a particle moving along a straight line is shown below.

TO DETERMINE

The average velocity of the particle in km/h.

EVALUATION

We add the points A , B , C in the figure

The distance covered by the particle between t = 0 and t = 100 sec

= Area of the triangle Δ OAB

= Area of the triangle Δ OAC + Area of the triangle Δ ABC

$\displaystyle \sf{ = \bigg( \frac{1}{2} \times 50 \times 100 \bigg)+ \bigg( \frac{1}{2} \times 50 \times 100 \bigg)}$

$\displaystyle \sf{ = 2500 + 2500}$

$\sf{= 5000}$

Now total time taken = 100 sec

Hence the required average velocity of the particle

$\displaystyle \sf{ = \frac{ Total \: distance \: covered }{Total \: time \: taken} }$

$\displaystyle \sf{ = \frac{ 5000 }{100} \: \: m/s}$

$\displaystyle \sf{ = 50 \: \: m/s}$

$\displaystyle \sf{ = \frac{ 50 \times 3600 }{1000} \: \: km/h}$

$\displaystyle \sf{ =180 \: \: km/h}$

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