Question

A speed skater moving across frictionless ice at 10.0 m/s hits a 5.0 m wide patch of rough ice. she slows steadily, then continues on at 7.0 m/s. what is her acceleration on the rough ice?

Answer 1

To calculate the acceleration of the skater on the rough ice, we use the equation

$v^2= u^2 + 2as$

Here, u is initial speed when she hits the patch of ice and its value is 10 m/s and v is final speed when she left the patch of ice and its value is given 7.0 m/s and s is the width of patch of ice and its value is 5.0 m.

Substituting these values in above equation we get,

$(7 m/s) ^2 = (10 m/s)^2 + 2 a \times 5.0 m \\\\ a = \frac{(70 - 100)(m/s)^2 }{ 10 m} = 3.0 m/s^2$.

Thus, the acceleration of skater on the rough ice is $3.0 m/s^2$