Question

a motorcyclist is coasting with the engine off at a steady speed of 28.5 m/s but enters a sandy stretch where the coefficient of kinetic friction is 0.65. part a will the cyclist emerge from the muddy stretch without having to start the engine if the sand lasts for 14 m ? will the cyclist emerge from the muddy stretch without having to start the engine if the sand lasts for 14 ? no yes

Answer 1

Yes, the cyclist will emerge from the muddy stretch without having to start the engine if the sand lasts for 14 with a final velocity of 31.47 m/s

Initial Speed (u) = 28.5 m/s

Coefficient of kinetic friction(µ) = 0.65

Distance traveled (s) = 14 m

Acceleration (a) = -µg = -0.65*9.8 = -6.37 m/$s^{2}$

Now, Applying the 3rd equation of motion, we have:

$v^{2} -u^{2} =2as$

$v^{2} -(28.5)^{2} = 2*(-6.37)*14\\\\v^{2} = 178.36 + 812.25 = 990.61\\\\v = 31.47$

Hence, the final speed will be 31.47 m/s

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