Question

A car start from rest and acquire avelocity of 54 km/ he in 2sec find acceleration ,distance travelled ,if mass of car is 1000g what is the force acting on it

Answer 1

Initial velocity ,u = 0 m/s

Final velocity , v = 54 km/h = 15 m/s

Time ,t = 2 s

Mass of car ,m = 1000 g = 1 kg

Apply 1st equation of motion ,

⇒ v = u + at

⇒ 15 = 0 + a(2)

⇒ 2a = 15

⇒ a = 7.5 m/s²  $\pink{\bigstar}$

Apply 2nd equation of motion ,

⇒ s = ut + ¹/₂ at²

⇒ s = (0)(2) + ¹/₂ (7.5)(2²)

⇒ s = 15 m  $\blue{\bigstar}$

Apply Newton Second Law ,

⇒ F = ma

⇒ F = (1)(7.5)

⇒ F = 7.5 N  $\orange{\bigstar}$

Answer 2

$\tt {\pink{Given}}\begin{cases} \sf{\green{Initial \: Velocity=0 \: m/s}}\\ \sf{\blue{Final \: Velocity=54 \: km/hr = 15 \: m/s}}\\ \sf{\orange{Time=2 \: seconds}}\\ \sf{\red{Mass=1000 \: g = 1 \: kg}}\\ \sf{\gray{Force= \:? }}\end{cases}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

AnsWer :

$\: \: \: \: \qquad\tiny\dag \: \underline{\textsf{ \textbf{ By using first equation of motion : }}}$

$:\implies\sf v = u + at$

$:\implies\sf 15= 0+ a(2)$

$:\implies\sf 2a = 15$

$:\implies\sf a = \dfrac{15}{2}$

$:\implies \underline{ \boxed{\sf a = 7.5 \: m/s^{2}}}$

$\underline{\textsf{ Hence,acceleration of the body is 7.5 m/s ^2 }}.$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

$\: \: \: \: \qquad\tiny\dag \: \underline{\textsf{ \textbf{ By using third equation of motion : }}}$

$\dashrightarrow\:\: \sf v^2 = u + 2as$

$\dashrightarrow\:\: \sf (15)^2 = (0)^{2} + 2(7.5)(s)$

$\dashrightarrow\:\: \sf 225= 0 + 15s$

$\dashrightarrow\:\: \sf 15s = 225$

$\dashrightarrow\:\: \sf s = \dfrac{225}{15}$

$\dashrightarrow\:\: \underline{ \boxed{ \sf s = 15 \: m }}$

$\underline{\textsf {Hence,distance covered by the body is 15 m}}.$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

$\: \: \: \: \qquad\tiny\dag \: \underline{\textsf{ \textbf{ By applying newton's second law : }}}$

$\leadsto \sf F = ma$

$\leadsto \sf F = 1 \times 7.5$

$\leadsto \underline{ \boxed{\sf F = 7.5 \: N}}$

$\underline{\textsf {Hence,the force acting on the body is 7.5 N}}.$