Question

in an automobile crash test, a vehicle is moving at a speed of 13.4m/s as it hits a reinforced concrete wall. assuming that the wall is not deformed by th empact of the crash, the vehicle comes to rest as the front end collapses straight-in towards the driver (a test dummy) from a distance of 100 cm
a) the magnitude of the vehicle's accleration is equal to
b)how much time passed as the vehicle slowed down from 30mi/hr to 0 mi/hr
c)is the vehicle's acceleration directed antiparallel to the vehicle's veclo
ity

Answer 1

a) to find the magnitude of the acceleration, use the formula
\[v ^{2}=u ^{2}+2as\]
where v is final velocity (zero, as the car came to a rest), u is initial velocity (13.4m/s) a is acceleration, and s is displacement (0.100m as this is how far the car traveled while decelerating)
solve for a:
\[a=\frac{ v ^{2}-u ^{2} }{ 2s }\]
and now you can substitute in the values for v, u, and s. You'll get a as a negative, but remember it just asked for magnitude, so you'd take the absolute value (or just drop the negative sign).

Answer 2

b) now that we have the acceleration, we can easily find the time t from (v is still final velocity, u is initial velocity, a is acceleration)
\[v=u+at\]
solve for t:
\[t=\frac{ v-u }{ a }\]

Answer 3

c) What do you think? Is the acceleration acting in the same direction as velocity, or the opposite direction? The fact that the acceleration was negative is a hint.