Question

A vehicle is traveling along a road and begins accelerating at 1.4 m/s2. After traveling 350 m at this acceleration, the velocity of the car is 32 m/s. What was the speed of the car when it began accelerating?

Answer 1

To find the initial speed of the car when it began accelerating, we can use the following kinematic equation:

v^2 = u^2 + 2as

where: v = final velocity = 32 m/s u = initial velocity (unknown) a = acceleration = 1.4 m/s^2 s = distance traveled = 350 m

Rearranging the equation, we get:

u^2 = v^2 - 2as

Substituting the given values:

u^2 = (32 m/s)^2 - 2 * (1.4 m/s^2) * (350 m) u^2 = 1024 m^2/s^2 - 980 m^2/s^2 u^2 = 44 m^2/s^2

Taking the square root of both sides, we find:

u = √(44 m^2/s^2) u ≈ 6.63 m/s

Therefore, the speed of the car when it began accelerating was approximately 6.63 m/s.