Question

A car start from rest and acquire a velocity of 54 km/h in 2 sec. Find
(i) the acceleration
(ii) distance travelled by car assume motion of car is uniform
(iii) If the mass of the car is 1000 Kg,what is the force acting on it?​

Answer 1

Given:-

• initial velocity (u) = 0m/s
• final velocity (v) = 54 km/h

• 54 × $\sf\dfrac{5}{18}$ = 15m/s (to convert km/hr into m/s we multiply the value with $\sf\dfrac{5}{18}$ )

• time (t) = 2sec.
• mass = 1000kg

Acceleration :-

$\underline{\boxed{\sf acceleration = \dfrac{final\: velocity-initial \:velocity}{t}}}$

$\longrightarrow$ Acceleration = $\sf\dfrac{15-0}{2}$

$\longrightarrow$ Acceleration = 15/2

$\longrightarrow$ Acceleration = 7.5m/s²

Distance:-

$\underline{\boxed{\sf S = ut+\dfrac{1}{2}at²}}$

here,

• s = distance
• u = initial velocity
• t = time taken
• a = acceleration

$\longrightarrow$ S = (0)(2) + $\sf\dfrac{1}{2}$ × (7.5)(2)²

$\longrightarrow$ S = 7.5×2

$\longrightarrow$ S = 15m

Force on the car:-

$\underline{\boxed{\sf Force = mass × acceleration}}$

$\longrightarrow$ Force = 1000×7.5

$\longrightarrow$ Force = 7500N

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Additional information:-

• when there is a change in rate of momentum we experience a force. This force can be calculated by:-

$\underline{\boxed{\sf Force = \dfrac{mv-mu}{t}}}$

here,

• final momentum = mv = mass × final velocity
• initial momentum = mu = mass × initial velocity