"a drag racing car starts from rest at t= 0 and moves along astraight line with velocity given by V = bt^2 where b isconstant. The expression for the distance traveled by this car from its position at t = 0 is
a)bt^3
b)bt^3/3
dx/dt = b t^2
so
x = (1/3) b t^3 + starting x
To find the expression for the distance traveled by the car, we need to integrate the velocity function with respect to time.
Given that the velocity function is V = bt^2, we can integrate it with respect to time to find the displacement function (distance traveled) as follows:
∫(V dt) = ∫(bt^2 dt)
To integrate this function, we use the power rule of integration. According to the power rule, the integral of t^n with respect to t is (1/(n+1)) * t^(n+1).
Applying the power rule to the integral, we have:
∫(bt^2 dt) = (b/3) * t^3 + C
Where C is the constant of integration.
Therefore, the expression for the distance traveled by the car from its position at t = 0 is (b/3) * t^3 + C.
In this case, the correct option would be b) bt^3/3, as it matches the expression derived from the integration.