1. A bus is travelling along a straight road at 25 m/s (90 km/h) when the driver sees a deer on the road and slams on the breaks. This causes a constant deceleration (a negative acceleration) ofk m/s^2. It takes the bus 5 seconds to stop. How far does the bus travel before coming to a stop?

Let t=0 at the moment the bus driver slams on the breaks.

Let v(t) be the velocity of the bus at time t(measured in m/s).

Let s(t) be the position of the bus at time t (measured in meters), and let's choose s(0)=0.

a. Find v(0) in m/s

V (5) = 0 V(5) = s(5) V(0) = 0 V (5) = 0 s (5) = 0\fs(t) =-5t^2 + 25 t + 5 s(t) = -5 t^2 + 25t s(t) = -5/2 t^2 + 25t s(t) = 25/2 t^2 - 5 t s (t) =-5/2 t^2 - 5tv(25) v (5) v(0) s(0) s (5)\fWhich of the following statements are TRUE? Select all that apply. O The most general antiderivative of f (x) = 2e* + 16x + 3 is given by F (x) = 2e* + 4x4+3x+C. O If F (x) is an antiderivative of f (x) and G (x) is an antiderivative of g (x), then: If (x) . 8 (x) dx = F (x) . G(x) + C O If F (x) is an antiderivative of f (x) and G (x) = F (x) + 7, then G (x) is also an antiderivative f (x). O 2x-'dx = X-3x 6x2 2x3 - + C O If F (x) is an antiderivative of f (x) and G (x) is an antiderivative of g (x), then: If ( x) + 8 (x)) dx = F(x) + G(x) + C O An antiderivative of a linear function is a linear function. An antiderivative of f (x) = 3 sin x is F (x) = -3 cos x + 2n O If F (x) is an antiderivative of f (x), then: J xf ( x) dx = xF (x) +C An antiderivative of f (x) = 6Vx + 3 is F (x) = 4(x + 3)z