A cyclist enters a curve of 30m radius at a speed of 12 ms-1. She applies the brakes and decreases
her speed at a constant rate of 0.5ms-2. Calculate the cyclist’s centripetal (radial) and tangential
accelerations when she is travelling at a speed of 10 ms-1
To calculate the cyclist's centripetal acceleration, we can use the formula:
a_c = v^2 / r
Where:
a_c = centripetal acceleration
v = velocity
r = radius of the curve
Plugging in the values:
a_c = (10)^2 / 30
a_c = 100 / 30
a_c = 3.33 ms^-2
Next, to calculate the tangential acceleration, we can use the formula:
a_t = -0.5ms^-2 (as it is decreasing)
Therefore, the cyclist's centripetal acceleration is 3.33 ms^-2 and the tangential acceleration is -0.5 ms^-2.