Question

A car travelling at a uniform speed of 20 m/s approaches a signal. The driver applies the

brake and the car retards uniformly at the rate of 2 m/s2. How much time will be taken

by the car to come to rest?​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Time\:taken=10\:sec}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Initial \: speed(u) = 20 \: m/s \\ \\ \tt: \implies Acceleration(a) = - 2 \: {m/s}^{2} \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Time \: taken(t) =?$

• According to given question :

$\tt \circ \: Final \: velocity = 0 \: m/s \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies 0 = 20 + ( - 2) \times t \\ \\ \tt: \implies - 20 = - 2 \times t \\ \\ \tt: \implies t = \frac{ - 20}{ - 2} \\ \\ \green{\tt: \implies t = 10 \: sec} \\ \\ \green{\tt \therefore Time \: taken \: to \: stop \: car \: is \: 10 \: sec}\\\\ \blue {\bold{Some \: related \: formula }} \\ \orange{\tt \circ \: s = ut + \frac{1}{2} {at}^{2}} \\ \\ \orange{\tt \circ \: {v}^{2} = {u}^{2} + 2as}$

Answer 2

Given :-

Initial speed of a car (u) = 20m/s

Final velocity (v)=0 [ car come in rest ]

Acceleration (Retardation ) = -2m/s^2

To find

Time taken to stop the car !

$\dag{\underline{\sf {By \ first \ equation \ of \ motion}}}$

$\bigstar{\boxed{\textsf{\textbf{v=u+at}}}}$

where !

v= Final velocity

u= initial velocity

t= Time taken

a = Acceleration

• Now find the time required to come car in rest

$\longmapsto\sf v=u+at\\ \\ \longmapsto\sf 0=20 + (-2)\times t\\ \\ \longmapsto\sf -20= -2\times t\\ \\ \longmapsto\sf \cancel{\dfrac{-20}{-2}}=t\\ \\ \longmapsto\sf t= 10 sec$

$\bigstar{\underline{\textsf{\textbf{Time \ taken \ to \ stop \ the \ car = 10 \ seconds }}}}$