Question #301041

A car starts to move at rest. It travels first 10 seconds with a constant acceleration of 2ms^-2 and the next one minute with the obtained constant velocity. During the final 30 seconds, it decelerates with a constant rate and comes to rest. Find the average velocity of the car.

1
Expert's answer
2022-02-23T08:32:15-0500

Explanation and Calculation


  • The total time is 10s+60s+30s=100s\small 10 \,s+60\,s+30\,s = 100\,s
  • And the maximum speed it achieves with that acceleration is

v=u+at=+\qquad\qquad \begin{aligned} \small v&=\small u+at\\ &=\small + \end{aligned} v=u+at=0+2×10=20ms1\qquad\qquad \begin{aligned} \small v&=\small u+at \\ &=\small 0+2\times10\\ &=\small 20\,ms^{-1} \end{aligned}

  • Now if we draw the v - t graph if this motion then the area which is the total distance travelled is

A=12×(100+60)×v\qquad\qquad \begin{aligned} \small A &=\small \frac{1}{2}\times(100+60)\times v \end{aligned}

  • And then, the distance is known, you can calculate the average velocity by total distance / total time

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