Question

The graph below shows a displacement(m)-time(s) graph for a particle moving in a straight line.The speed of the particle in the first T seconds was half the speed of the particle in the last 3 seconds.Find the value of T.

Answer 1

The value of T = 6 sec

Explanation:

We need to find the relationship between displacement, speed and time

The formula relating the displacement to speed and time:

$\text{speed = }\frac{displacement}{time}$

For the first T seconds:

time = T

displacement = 4m

$speed_1\text{ = }\frac{4}{T}$

For the last 3 seconds:

time = 14 sec - 11 sec = 3 sec

displacement = 4 - 0 = 4 m

$speed_3\text{ = }\frac{4}{3}\text{ m/s}$

From the question:

The speed of the particle in the first T seconds was half the speed of the particle in the last 3 seconds

$\begin{gathered} speed_1\text{ = }\frac{1}{2}(speed_3) \\ \frac{4}{T}\text{ = }\frac{1}{2}(\frac{4}{3}) \\ \frac{4}{T}=\text{ }\frac{4}{6} \\ \frac{4}{T}=\text{ }\frac{4}{6} \\ \text{cross multiply:} \\ 4(6)\text{ = 4(T)} \\ 24\text{ = 4T} \end{gathered}$$\begin{gathered} \frac{24}{4}\text{ = }\frac{4T}{4} \\ T\text{ = 6 sec} \end{gathered}$