Answer:
A. -783752 J
B. -14250 N
C. 11.94 m/s
Explanation:
A. Work done is given as the change in kinetic energy, hence,
W = ΔKE
W = KE(final) - KE(initial)
KE(final) = 0 since the car comes to rest.
=> W = -KE(initial)
W = -½*m*u²
W = -½ * 1600 * 31.3²
W = -783752J
The negative indicates that the force responsible for the work is acting opposite the direction of the motion.
B. Work done is also given as:
W = F * d
Where F = Force
d = distance moved
=> F = W/d
F = -783752/55
F = -14250 N
The negative indicates that the force acts against the direction of motion.
C. The initial velocity, u, is now 33.5m/s.
Going back to the formula for work done in A,
W = KE(final) - KE(initial)
KE(final) is not zero in this case because the car doesn't come to rest before collision, hence,
W = ½*m*v² - ½*m*u²
Since the force is the same, then, work done is the same,
-783752 = ½*m*v² - ½*1600*33.5²
-783752 = ½*m*v² - 897800
½*m*v² = 897800 - 783752
½*m*v² = 114048
v² = (114048 * 2) / (1600)
v² = 142.56
v = 11.94 m/s