Question

A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation x(t)= α t2− β t3, where α = 1.40m/s2 and β = 5.05×10−2m/s3

A) What is the average velocity of the car for the time interval t=0 to t1=1.91s?

B) What is the average velocity of the car for the time interval t=0 to t2 = 3.99s?

C) Calculate the average velocity of the car for the time interval t1 = 1.91s to t2 = 3.99s

I don't know where to even start.

Answer 1

x = 1.40 t^2 - .0505 t^3
at t = 0, x = 0
at t = 1.91, x =1.40 * 1.91^2 - .0505 * 1.91^3 = 4.755 meters
so
4.755 meters in 1.91 seconds = 2.5 m/s

do the others the same way, find out how far it went in the time interval and divide by the time interval

Answer 2

Can you help me get started on C? I'm stuck there.

Answer 3

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.500 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 3.50 µC. They are released from rest when their centers are separated by 1.00 m.
(a) How fast will each be moving when they collide? (Hint: Consider conservation of energy and of linear momentum.