A car accelerates at the rate of 5 m/s2 .Find the increase in the velocity of the car in 2second. Find the velocity of the car after two seconds if it starts from rest.
Answers
Answer:
The First Method starts by defining the acceleration provided above as the second derivative with respect to position x. An integral with respect to time is taken to arrive at an equation of velocity (the first derivative of position). This introduces a constant that must be accounted for, namely c. It is assumed that at time 0 the velocity is 0 and thus c is found to be 0. It is important to understand that depending on the scenario this may not always hold.
x'' = 5
x' = 5t + c
Assume at t = 0 that x' = 0:
x' = 0 = 5*(0) + c
Thus c = 0
Therefore our equation of velocity for any time t is:
v(t) = x' = 5t
Specifically, at t = 2 we have:
v(2) = x' = 5(2) = 10m/s
The Second Method provided below is commonly taught in highschool physics as part of a set of equations referred to as one dimensional kinematic equations. The relevant equation is provided with the same assumption as above; namely, that initial velocity is equal to zero.
V_final = V_initial + at
Assume V_initial = 0 and plug 5 in for acceleration:
V_final = 5t
Specifically at t = 2 we have:
V_final = 10 m/s
Explanation:
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