Determine the force required to bring an 8-ton truck traveling at 50 mph to rest in 5 seconds. How far does it travel?
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First, we need to convert the weight of the truck from tons to kilograms and the speed from mph to m/s.
1 ton = 907.185 kg, so 8 tons = 8 * 907.185 = 7257.48 kg
1 mph = 0.44704 m/s, so 50 mph = 50 * 0.44704 = 22.352 m/s
The force required to stop the truck can be calculated using the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
The acceleration is the change in velocity divided by the time it takes for the change to occur. In this case, the truck is going from 22.352 m/s to 0 m/s in 5 seconds, so the acceleration is (0 - 22.352) / 5 = -4.4704 m/s².
The negative sign indicates that this is a deceleration, or a slowing down.
So the force required is F = ma = 7257.48 kg * -4.4704 m/s² = -32442.6 N.
The negative sign indicates that the force is acting in the opposite direction to the motion of the truck, which makes sense because it's a stopping force.
The distance the truck travels can be calculated using the formula d = vt + 0.5at², where d is the distance, v is the initial velocity, a is the acceleration, and t is the time.
So the distance is d = 22.352 m/s * 5 s + 0.5 * -4.4704 m/s² * (5 s)² = 111.76 m - 55.88 m = 55.88 m.
So the force required to stop the truck is 32442.6 N, and the truck travels 55.88 m before coming to rest.