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A motorbike initially travelling at a velocity of 4m/s accelerates to a velocity of 12m/s The motorbike travels a distance of 16 m during this time. Calculate the acceleration of the motorbike.

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A motorbike initially travelling at a velocity of 4m/s accelerates to a velocity of 12m/s
The motorbike travels a distance of 16 m during this time.
Calculate the acceleration of the motorbike.

A motorbike initially travelling at a velocity of 4m/s accelerates to a velocity of 12m/s The motorbike travels a distance of 16 m during this time. Calculate the acceleration of the motorbike.

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SheldonElite · Tutor for 8 years

Answer

The proper acceleration of the motorbike is a = 4 m/s^2.

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Acceleration can be calculated using the formula a = (v_f - v_i)/t, where a = acceleration, v_f = final velocity, v_i = initial velocity, and t = time. However, in this problem, we are not given the time directly. Instead, we first need to calculate the time using the formula for distance (s) in uniformly accelerated motion: s = v_it + 0.5a*t^2. This problem requires us to solve first for time and then use that result to calculate acceleration.<br /><br />In this case:<br />Initial velocity (v_i) = 4 m/s,<br />Final velocity (v_f) = 12 m/s,<br />and the total distance (s) = 16 m.<br /><br />Initial step involves rearranging the formula for distance to solve for time.'<br /><br />Given, s = v_it + 0.5a*t^2 <br />=> t = (s - 0.5vat)/v_i (equation 1)<br /><br />But we don't have acceleration and the equation includes the term of 'time(t)', we need to bring the other equation: v_f = v_i + t*a (equation 2).<br /><br />From equation 2: t = (v_f - v_i)/a (equation 3), and now substitute EQ.3 into EQ.1, we could get the relation of acceleration (a) only and then find the specific value.<br /><br />Calculation:<br /><br />Rearrange equation 2 to get:<br />a = (v_f - v_i)/t,<br />Now substitute this into equation 1 to get acceleration:<br /><br />=> A = [(v_f - v_i)^2 / (2 * (s - (v_i*(v_f - v_i)/ (v_f - v_i()))))] ---- Apply the value into equation becomes<br /> = [(12 - 4)^2 / (2*(16 - 4*(12 - 4)/(12 - 4)))]<br /> = (8^2 / (2*(16 - 8))<br /> = 64 / 16<br /> = 4 m/s^2
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