of a Maserati is proportional to? Words problems review for exam?
How do I solve each one?
1. The acceleration of a Maserati is proportional to the difference between 250 km/h and the velocity of this sports car. if this machine can accelerate from rest to 100km/h in 10s, how long will it take for the car to accelerate from rest to 200 km/h?
2. Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = - kv.
a) Show that its velocity and position at time t are given by
v(t)=v0e^(-k*t)
and x(t) = x0 + (v0/k) (1-e^(-kt).
b) Conclude that the body travels only a finite distance, and find that distance.
3. Suppose that a motorboat is moving at 40ft/s when its motor suddenly quits, and that 10s later the boat has slowed to 20ft/s. Assume, as in Problem 2, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?
4. A motorboat weighs 32,000 pounds and its motor provides a thrust of 5000 pounds. Assume that the water resistance is 100 pounds for each foot per second of the speed v of the boat.
Then 1000(dv/dt) = 5000 - 100 v.
If the boat starts from rest, what is the maximum velocity that it can attain?
How do I solve each one?
1. The acceleration of a Maserati is proportional to the difference between 250 km/h and the velocity of this sports car. if this machine can accelerate from rest to 100km/h in 10s, how long will it take for the car to accelerate from rest to 200 km/h?
2. Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = - kv.
a) Show that its velocity and position at time t are given by
v(t)=v0e^(-k*t)
and x(t) = x0 + (v0/k) (1-e^(-kt).
b) Conclude that the body travels only a finite distance, and find that distance.
3. Suppose that a motorboat is moving at 40ft/s when its motor suddenly quits, and that 10s later the boat has slowed to 20ft/s. Assume, as in Problem 2, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?
4. A motorboat weighs 32,000 pounds and its motor provides a thrust of 5000 pounds. Assume that the water resistance is 100 pounds for each foot per second of the speed v of the boat.
Then 1000(dv/dt) = 5000 - 100 v.
If the boat starts from rest, what is the maximum velocity that it can attain?