Question

A car moving on a straight road at 18 km /hr increase its velocity to 54 km / hr at a uniform rate in 10 s . Find the acceleration and distance moved in that tie .( hint-convert km /hr into m/sec first )
Initial speed u =18 km /hr =18000 m/ 36000 s =5 m / s
final speed v = 544 km/ hr = _______=_______

(i) Acceleration,a=______________=_________
(ii) Displacement,s=________________=_________________=________________

Answer 1

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

$\green{\tt{\therefore{Acceleration=1\:m/s^{2}}}}$

$\green{\tt{\therefore{Distance=100\:m}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Initial\:velocity(u) = 18 \: km/{h} \\ \\ \tt: \implies Final \: velocity(v) = 54 \: km/h\\\\ \tt:\implies Time(t)=10\:sec\\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Acceleration(a) = ? \\ \\ \tt: \implies Distance(s) = ?$

• According to given question :

$\tt \circ \: Initial \: velocity = 18\times \frac{5}{18}=5 \: m/s \\\\ \tt \circ \: Final \: velocity = 54\times \frac{5}{18}=15 \: m/s \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies 15 = 5 + a \times 10 \\ \\ \tt: \implies 15-5 = a \times 10 \\ \\ \tt: \implies t = \frac{10}{10} \\ \\ \green{\tt: \implies a=1 \:m/s^{2}} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies s = ut + \frac{1}{2} {at}^{2} \\ \\ \tt: \implies s = 5 \times 10 + \frac{1}{2} \times 1 \times {10}^{2} \\ \\ \tt: \implies s = 50 + 50 \\ \\ \green{\tt: \implies s = 100 \: m}$

Answer 2

Given :-

$\texttt{Initial velocity(u) = 18 km/h = 5 m/s}\\\\\texttt{Final velocity(v) = 54 km/h = 54}*\tt{\frac{5}{18}}\texttt{ = 15 m/s}\\\\\texttt{Time(t) = 10 s}$

To find :-

$\texttt{The acceleration of the car and distance}\\\texttt{travelled by it.}$

Solution :-

$\text{We know :}$

$\tt{v=u+at}$

$\text{Putting the known values :}$

$\tt{15=5+a(10)}\\\\\tt{\implies 15=5+10a}\\\\\tt{\implies 10=10a}\\\\\boxed{\tt{\implies a=1\ m/s^2}}$

$\text{We also know that,}$

$\tt{s=ut+\frac{1}{2}at^2 }$

$\text{Putting the known values :}$

$\tt{s=5*10+\frac{1}{2}*1*(10)^2 }\\\\\tt{\implies s=50+\frac{100}{2} }\\\\\tt{\implies s=50+50}\\\\\tt{\boxed{\implies s= 100\ m}}$