The speed `v` of a car moving on a straight road changes according to equation, `v^2 = 1 + bx`, where `a and b` are positive constants. Then the magnitude of acceleration in the course of such motion : (x is the distance travelled).

Options

A. increases
B. decreases
C. stay constant
D. first decreases and then increases

Answer

C

Explanation

`v^2 = a + bx`
`v` increase as `x` increases
`a = v (dv)/(dx) = (1)/(2) (d)/(dx) (v^2) = (b)/(2)`
Hence, acceleration is constant.