Question

1.An object moves in a straight line starting from rest.There are two stages in the journey

(a)it gains speed uniformly for 2.0s and attains a speed of 8.0ms-1

(b)it continues at this speed for a further 1.5

Draw a sketch graph of speed against time

Find(1)the acceleration in stage (a)

(2)the acceleration in stage (b)

(3)the total distance moved during stages (a)and(b)

Answer 1

(1) The acceleration:

$$a=\frac vt=\frac 82=4\text{ m/s}.$$

(2) The acceleration at stage b is zero since the velocity does not change.

(3) The total distance:

$$D=d_a+d_b=\frac{at^2}{2}+v\tau,\\\space\\ D=\frac{4·2^2}{2}+8·1.5=20\text{ m/s}.$$