a) A car is driven at 30 m/s for 30 seconds and 70 m/s for the next 30 seconds.

Question

a) A car is driven at 30 m/s for 30 seconds and 70 m/s for the next 30 seconds. What is its average speed of the car for the last 40 seconds of the drive.

b) A mass is dropped from a height of 45 m and undergoes freefall. How long does it take before it hits the ground?

c) An object in uniform circular motion travels in a circle with radius of 36 m and a period of 6 s. What is its acceleration?

d) An object has a position given by r= ti hat +(t-2)^4 j hat (m/s). its acceleration at time t=3 s is?
e) In uniform circle motion which of the following is true?
1. the acceleration is zero
2. the velocity is zero
3. the velocity is constant
4. the magnitude of velocity is constant
5. the displacement is zero

f) For general projectile motion, which stament is true?
1. its acceleration is zero
2. its velocity is zero
3. its velocity and acceleration are both zero
4. the horizontal component of its acceleration is zero.
5. all of the above

Explanation / Answer

Speed v = 30 m / s            v ' = 70 m / s (a). Average speed V = total distance in 40 s / time                                   = [ (vx 10 ) + (v ' x 30 ) / 40                                   = 60 m / s (b).height h = 45 m Required time t = [ 2h / g ]                          = 3.03 s (c).Radius r = 36 m Period T = 6 s Angular speed = 2 / T                           = 1.047 rad / s Accleration a = r 2                      = 39.47 m / s 2 (d). Position r = t i +(t-2) 4 j Velocity v = dr / dt                 = 1 i + 4( t-2) 3 j             Accleration a = dv / dt                      = 12 ( t-2) 2 j Accleration at t= 3 s is a = 12 ( 3-2) 2 j                                        = 12 m / s 2 (e). the magnitude of velocity is constant (f). the horizontal component of its acceleration is zero
                     = 39.47 m / s 2 (d). Position r = t i +(t-2) 4 j Velocity v = dr / dt                 = 1 i + 4( t-2) 3 j             Accleration a = dv / dt                      = 12 ( t-2) 2 j Accleration at t= 3 s is a = 12 ( 3-2) 2 j                                        = 12 m / s 2 (e). the magnitude of velocity is constant (f). the horizontal component of its acceleration is zero

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