If the velocity is constant then the acceleration of the object is zero.
Thus when we apply the equation
It remains
or equivalent
Answer: 16.09m/s
Explanation:
Given the acceleration a(t) = 10/(t+1), to derive the velocity function, we need integrate the acceleration function.
v(t) = integral{10/t+1}dt
Since all constants always come out of the integral, the equation becomes;
v(t) = 10integral{1/t+1}dt
One of the integral law is that if the numerator of the function to be integrated is the differential of the denominator, the resulting answer will be natural logarithm of the denominator i.e ln(t+1) since the denominator is ln(t+1) and if differentiated will give us 1 which is the numerator hence, the reason for the answer ln(t+1)
v(t) = 10ln(t+1)
@ t= 4, the velocity of the particle
v(4) = 10ln(4+1)
v(4) = 10ln5
v(4) = 16.09m/s²
Therefore, the velocity of the particle at time t=4 is 16.09m/s
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