Question

A car moving at 15 m/s suddenly brakes at a distance of 2.0 m from another car that comes across suddenly. What is the average force generated by a car's seat belt on a passenger with a mass of 90 kg when the car is stopped right when the two cars hit?

Answer 1

From the Question,

• Initial Velocity,u = 15 m/s

• Distance Covered,s = 2 m

• Mass of the total system,M = 90 Kg

Since,

The car comes to a halt,the final velocity of the car will be tending to zero » v = 0 m/s

Using the Relation,

$\huge{ \sf{v {}^{2} - u {}^{2} = 2as }} \\ \\ \large{ \hookrightarrow \: \sf{0 {}^{2} - u {}^{2} = 2as}} \\ \\ \large{ \hookrightarrow \: \boxed{ \boxed {\sf{ \blue{a = - \frac{ {u}^{2} }{2s} }}}}}$

Substituting the values,we get :

$\large{ \sf{a = - \dfrac{ {15}^{2} }{2(2)} }} \\ \\ \large{ \mapsto \: \sf{a = - \frac{225}{4} }} \\ \\ \large{ \mapsto \: \boxed{ \boxed{\sf{ \green{a = \: - 56.25 \: m {s}^{ - 2}} }}}}$

We Know that,

$\huge{ \boxed{ \boxed{ \tt{ \blue{F = Ma}}}}}$

Substituting the values,we get :

$\large{ \leadsto \: \tt{F = (90)( - 56.25)}} \\ \\ \huge{ \leadsto \: \boxed{ \boxed{\tt{F = - 5062.5 \: N}}}}$

The car experiences a force of magnitude - 5062.5 N