AP Physics help

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To solve AP Physics questions we need to review some of the important formulas.

Average speed: v = ds/dt

Velocity: It is same as speed but it has direction because it is a vector quantity.

Acceleration:      a = dv/dt

An object moving with constant velocity has zero acceleration.

Fundamental kinematic equations:
          Vf = Vi + at
          S = Vi + ½ at^2
          Vf^2 = Vi^2 + 2aS
Where, Vf = final velocity
          Vi = Initial velocity
          S = distance
          a = acceleration
And   t = time

Example: A dog sits 5.4 m from the centre of a merry-go-round. If the dog undergoes a 3.6 m/s^2 centripetal acceleration, what is the dog's linear speed? Answer in units of m/s.

Solution: We have given,
Centripetal acceleration, a = 3.6 m/s^2
And radius of the circular path, r = 5.4 m
We have the equation,
Centripetal acceleration, a = V^2/r
Where, V = Linear velocity.
                                      3.6 = V^2/5.4
                                      V = 4.4 m/s.
Example: A car is travelling at 85 km/h.The driver stomps on the gas pedal and accelerates up to a speed of 95 km/h. It took 3.5 seconds to reach this speed, what is the average acceleration?

Solution: We have given,
          Initial velocity, Vi = 85 Km/hr = 85 x 60 x 60 /1000 m/s
                                                          = 306 m/s
          Final velocity, Vf = 95 Km/hr = 95 x 60 x 60/1000 m/s
                                                          = 342 m/s
          Now, we have the equation for acceleration,
                   a = (342 – 306)/3.5 = 10.28 m/s^2.


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