# Answer to Question #68876 in Mechanics | Relativity for Becca

Question #68876

Our Addition Problem this week will deal with an asteroid the "size of Texas" heading our way. Our asteroid is heading toward earth at 22,000 mph with a mass of 6.2 x 1021 kg. Instead of a misfit crew of oil drillers we send a small intrepid spacecraft to nudge it off course. After setting down on the asteroid it will give a constant force of 5.0 N. We only need to change the velocity of the asteroid by 0.30 cm/s to have it miss the Earth. How long must the force act on the asteroid to avert disaster?

Expert's answer

Constant force affects constant acceleration, which changes the velocity according to:

v=v_0+at

Following the starting equation we can find the time required for the changing of the velocity:

t=(v-v_0)/a=(m(v-v_0))/F=(m∙∆v)/F

Thus, the time is calculated to be:

t=(3×〖10〗^(-3) m/s)/(5.0 N)∙6.2×〖10〗^21

v=v_0+at

Following the starting equation we can find the time required for the changing of the velocity:

t=(v-v_0)/a=(m(v-v_0))/F=(m∙∆v)/F

Thus, the time is calculated to be:

t=(3×〖10〗^(-3) m/s)/(5.0 N)∙6.2×〖10〗^21

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