Question

calculate the acceleration of a car that goes from rest to 100m/s while travelling a distance of 1000m​

Answer 1

Given :-

 A body starts from rest i.e Initial velocity (u = 0 m/s) . Final velocity (v = 100 m/s)

Distance travelled (s = 1000m)

To find :-

Acceleration of the car .

Solution  :-

As we have Distance travelled, Initial, Final velocity we need to calculate Acceleration of the car. We can solve by using Third equation of motion.  

$\: \: \: \: \: \: \: \: \: \boxed{ \underline{ \pink {\dag \: {\pmb {{v {}^{2} - u {}^{2} = 2as}}}}}}$

where,

v= final velocity

u = initial velocity

a = acceleration

s = distance covered

¤Substituting the values,  

$\: \bf \implies\: (100) {}^{2} - (0) {}^{2} = 2 \times a \times 1000$

$\bf \implies\: (100) {}^{2} = 2 \times a \times 1000$

$\: \bf \implies\:100 \times 100 = 2 \times a \times 1000$

$\: \bf\implies\: 1 \not0 \not0 \times 1 \not00 = 2 \times a \times 1 \not0 \not0 \not0$

$\: \bf\implies \: 10 = 2 \times a$

$\bf \implies\: \dfrac{10}{2} = a$

$\:  \boxed{ \bf \red{ \dag \: a = 5 \: m/s {}^{2} }}$

So, acceleration of the car is 5 m/s²

Know more 3 Equations of motion:-

$\boxed{ \underline \dag \pmb{ \pink {v = u + at }}}$

$\boxed{ \underline \dag \pmb{ \pink {s = ut +  \frac{1}{2} at {^{2} }}}$

$\: \: \: \: \: \: \: \: \: \boxed{ \underline{ \pink {\dag \: {\pmb {{v {}^{2} - u {}^{2} = 2as}}}}}}$

where,

v= final velocity

u = initial velocity

a = acceleration

s = distance covered

t = time taken