Question

A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at t=0) the car was at x=0, where x is the position of the car at any time t. Find acceleration of car at time t=15 sec and t=55 sec (1) (0 ,5/2) m/s2 (2) (0, 0.4) m/s2 (3) (0, -0.4) m/s2 (4) (0,0.2) m/s2​

Answer 1

Explanation:

Displacement is positive when graph is above x-axis. Thus maximum displacement occurs at 50 second, till which graph is above axis. After that displacement needs to be subtracted from total. Thus maximum displacement = Area under curve till 50 seconds = Area of triangle till times 10 seconds + area of rectangle from time 10 seconds till 20 seconds + area of trapezium from time 20 seconds till 30 seconds + area of triangle from time 30 seconds till 50 seconds.

s=21×4×10+4×10+21×10×(4+8)+21×20×8

   =20+40+60+80=200 m

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