# Math Help - show time travelled with uniform speed

1. ## show time travelled with uniform speed

a lift starts from rest with constant acceleration 4m/s squared. it then travels with uniform speed and finally comes to rest with constant retardation 4m/s squared. the total distance travelled is D an the total time is t

(i) show that the time for which it travelled with uniform speed is
Ö t squared-d

2. Originally Posted by ronan116
a lift starts from rest with constant acceleration 4m/s squared. it then travels with uniform speed and finally comes to rest with constant retardation 4m/s squared. the total distance travelled is D an the total time is t

(i) show that the time for which it travelled with uniform speed is
Ö t squared-d
here is a very brief outline of an approach:

Motion 1:
u = 0
a = 4 m/s^2
$t = t_1$
$v = v_1$
$x = x_1$

Motion 2:
$x_2 = v_1 t_2$

Motion 3: By symmetry with motion 1
$u = v_1$
a = -4 m/s^2
$t = t_1$
v = 0
$x = x_1$

Given:

$t = 2 t_1 + t_2$ .... (1)

$D = 2 x_1 + v_1 t_2$ .... (2)

Use the motion data to get $x_1$ and $v_1$ in terms of $t_1$ and substitute into equation (2).

Then solve equations (1) and (2) simultaneously.