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

Step-by-step explanation:

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

The formula relating the displacement to speed and time:

`\text{speed = }(displacement)/(time)`

For the first T seconds:

time = T

displacement = 4m

`speed_1\text{ = }(4)/(T)`

For the last 3 seconds:

time = 14 sec - 11 sec = 3 sec

displacement = 4 - 0 = 4 m

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