The position of a particle is defined by St 2sint i 4cost

The position of a particle is defined by S(t) = 2sint i + 4cost j [t in radians] What is the magnitude of the particle\'s acceleration at t = Pi ? 2 00 2.56 314 4.00 A 60000 kg railcar moving at 1 km/h is instantaneously coupled to a stationary 40000 kg railcar What is the speed of the coupled cars? 0 40 km/h 0 60 km/h 0 88 km/h 1.0 km/h A mass of 10 kg .s suspended from a vertical spring with a spring constant of 10 N/m What is the period of vibration? 0.30s 0 60s 0 90s 6.3s

Solution

3.

v = ds/dt

= 2cost i - 4sint j

a = dv/dt

= -2sint i - 4costj

At t= pi, we get a = -2*sin pi i - 4*cos pi j

= 0 - 4*(-1) j

= 4j

Hence, magnitude of acceleration = 4

4.

By momentum conservation, 60000*1 = (60000 + 40000)*v

v = 0.6 km/h

5.

Time period T = 2*pi*sqrt(m/k)

= 2*3.14*sqrt(10/10)

= 6.3 s