Question

A racer accelerates from a stop so that its speed is 10t m/s t second after starting how far will the car go in 4 seconds?

Answer 1

Initial velocity is 0 and and final is 10 time is 4 sec then distance = average velocity/ time

Answer 2

Given:

A racer accelerates from a stop so that its speed is 10t m/s t second after starting.

To find:

How far will the car go in 4 seconds.

Solution:

According to the question,

$\frac{d y(t)}{d t}=10 t \\Here, y(t) is the distance traveled, and 't' varies from 0 to 4.\\On integrating both the sides with the respect to 't', we get:\\= \int_{0}^{4} d y(t)=\int_{0}^{4} 10 t d t\\=y(4)-y(0)=\left[5 t^{2}\right]_{0}^{4} \\\\ y(0) is zero as car is at rest at time 0.\\\\\rightarrow y(4) = 5(16) = 80m.$

Therefore, the distance traveled by the car is 80m.