Question

A car travels with uniform velocity of 30 m/s for 5 s. The brakes are then applied and the car comes to rest with a uniform retardation in a further 10 s. Draw a velocity-time graph and use it to find
(i) the distance to which the car travels after the brakes are applied and
(ii) distance travelled in first 5 s
(iii) total distance travelled
(iv) acceleration during the first 5 s and in last 10 s.

Answer 1

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Given

v1 = 30 m/s

t1 = 5 sec.

Let S be the distance travelled by tha cat after the application of brake.

Therefore the initial velocity of the car after applying the break becomes, u= 30m/s

Retardation of the car,

$a = \frac{v - u}{t} = \frac{(0 - 30)}{10} = \frac{ - 30}{10} \\ = - 3 \: m / {s}^{2} </p><p>$

According to the equation of motion,

${v}^{2} - {u}^{2} = 2as$

$0 - {30}^{2} = 2 \times ( - 3) \times s$

$s = \frac{ - 900}{ - 6} = 150 \: m</p><p>$

the distance travelled by the car after the breaks are applied is 150