Question

Suppose the speedometer of a vehicle covers the following speeds in kmh-1 at the end of successive intervals of 2 seconds, 37.8, 51.7, 63.3, 72.5, 79.8, 85.0, 89.0, 91.4. Plot the velocity – time graph for the journey.Obtain from your graph the distance covered in meters when the speed increased from 79 to 89kmh-1.Deduce the acceleration in ms-1 if the speeds are 49kmh-1, 69kmh-1 and 89kmh-1.

Answer 1

(1)

(2)

$s=\int{v(t)dt}$ or

$s\approx\frac{v_1+v_2}{2}\cdot\Delta t=\frac{21.94+24.72}{2}\cdot(14-9.7)=100.32(m)$

(3)

$a=\frac{dv(t)}{dt}$ or $a=k=\tan\alpha$

$a_1=\tan\alpha_1\approx1(m/s^2)$

$a_2=\tan\alpha_2\approx0.7(m/s^2)$

$a_3=\tan\alpha_3\approx0.27(m/s^2)$