1) The driving wheel of a bicycle is rotating at N = 206 revs per minute. If the

Question

1)

The driving wheel of a bicycle is rotating at N = 206 revs per minute. If there is no slippage between the wheel and the road, calculate the bicycle speed in km/h if the diameter of the wheel is 680mm.

2)

The position (in metres) of a particle is given by the equation.

What is the velocity of the body at a time 4.7 seconds (in m/s)

Remember, if your solution is negative, include this in your answer.

3)

The position (in metres) of a particle is given by the equation.

where the angle will be quoted in radians.

What is the velocity of the body at a time 1.0 seconds (in m/s)

Remember, if your solution is negative, include this in your answer.

4)

The position (in metres) of a particle is given by the equation.

What is the acceleration of the body at a time 2.9 seconds (in m/s2)

Remember, if your solution is negative, include this in your answer.

5)

For the first several seconds of time, a particle accelerates (in m/s2) from rest at a rate

What is the velocity at t = 2.3 seconds (in m/s)

6)

For the first several seconds of time, a particle accelerates (in m/s2) at a rate

If the initial velocity is 1 m/s, how far from the origin will the particle have moved at a time t = 4.4 seconds (in m/s)

Explanation / Answer

1)velocity=pi*D*N/60=3.14*0.68*206/60=7.334M/S

2)V=dS/dT=10t+4=10*4.7+4=51m/s

3)v=ds/dt=9cos3t =9cos 3=8.98m/s

4)a=d2s/dt2

=6t+12.8=6*2.9+12.8=30.2m/s^2

5)a=-t^2+6.5t

v=integral a dt

v=-t^3/3+6.5t^2/2

v=-2.3^3/3+3.25*2.3^2

v=-4.0556+17.1925=13.137m/s

6) acceleration at t=4.4 sec

a=-4.4^2+6*4.4=7.04m/s2

distance travelled=ut+0.5at^2

=1*4.4+0.5*7.04*4.4^2

=72.5472m

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