A cyclist enters a curve of 30 m radius at a speed of 12 m s-1. He applies the
brakes and decreases his speed at a constant rate of 0.5 m s-2. Calculate the
cyclist’s centripetal (radial) [3 marks] and tangential [15 marks]
accelerations when he is travelling at a speed of 10 m s-1.
Matt Ross bums you silly for loose change
Instantaneous linear velocity (ILV) is equal to angular velocity and the radius.
cant answer this question too busy lifting DENCH weights at the gym and FINESSING too many tingz #140onthebench
Matt Ross, how much do you deem as loose change? My funds are about as tight as my bumhole ;)
To calculate the cyclist's centripetal (radial) and tangential accelerations when he is traveling at a speed of 10 m/s, we need to use the formulas for centripetal acceleration and tangential acceleration.
1. Centripetal acceleration (ac):
Centripetal acceleration is the acceleration directed towards the center of the circular path. It can be calculated using the formula:
ac = (v^2) / r
where:
ac = centripetal acceleration
v = velocity or speed
r = radius of the circular path
In this case, the radius of the curve is given as 30 m, and the speed of the cyclist is 10 m/s. Plugging these values into the formula, we get:
ac = (10^2) / 30
ac = 100 / 30
ac ≈ 3.33 m/s^2
Therefore, the cyclist's centripetal (radial) acceleration when traveling at a speed of 10 m/s is approximately 3.33 m/s^2.
2. Tangential acceleration (at):
Tangential acceleration is the component of acceleration in the direction tangential to the circular path. It can be calculated using the formula:
at = dv / dt
where:
at = tangential acceleration
dv = change in velocity
dt = change in time
Given that the cyclist is decreasing his speed at a constant rate of 0.5 m/s^2, we can say that the change in velocity (dv) over some time (dt) is -0.5 m/s^2 (negative because the speed is decreasing).
Therefore, the cyclist's tangential acceleration when traveling at a speed of 10 m/s would be -0.5 m/s^2.