# show time travelled with uniform speed

• Nov 18th 2008, 11:41 AM
ronan116
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
• Nov 18th 2008, 04:18 PM
mr fantastic
Quote:

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
\$\displaystyle t = t_1\$
\$\displaystyle v = v_1\$
\$\displaystyle x = x_1\$

Motion 2:
\$\displaystyle x_2 = v_1 t_2\$

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

Given:

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

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

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

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