Question

calculate the acceleration of the object at point b using the velocity time graph? 25 m/s² 50 m/s² 2 m/s² 0 m/s²

Explanation:

Step1: Recall acceleration formula from v-t graph

Acceleration \( a \) is the slope of velocity - time (\( v - t \)) graph, given by \( a=\frac{\Delta v}{\Delta t}=\frac{v_f - v_i}{t_f - t_i} \).
From the graph, initial velocity \( v_i = 0\ m/s \) (at \( t = 0\ s \)), final velocity at point B: let's assume from the graph, at \( t = 25\ s \) (looking at the x - axis, if the x - axis is time in seconds and the y - axis is velocity in m/s, and the line goes from (0,0) to (25,50) maybe? Wait, but let's check the options. Wait, maybe the time at B is 25 s and velocity is 50 m/s? Wait, no, let's re - examine. Wait, the x - axis: let's see, the time scale, if the graph is a straight line from (0,0) to (25,50)? No, wait the options have 2 m/s². Wait, maybe the velocity at B is 50 m/s and time is 25 s? Wait, no, let's do it properly.
Wait, the formula for acceleration from \( v - t \) graph is \( a=\frac{\text{Change in velocity}}{\text{Change in time}} \).
From the graph, initial velocity \( v_i = 0\ m/s \) (at \( t = 0\ s \)), let's say at point B, time \( t = 25\ s \) and velocity \( v = 50\ m/s \) (assuming the y - axis is velocity and x - axis is time). Then \( \Delta v=v - v_i=50 - 0 = 50\ m/s \), \( \Delta t=t - t_i=25 - 0 = 25\ s \). Then \( a=\frac{50}{25}=2\ m/s^{2} \).

Step2: Calculate acceleration

Using \( a=\frac{v_f - v_i}{t_f - t_i} \), with \( v_i = 0\ m/s \), \( v_f = 50\ m/s \) (from the graph, assuming the velocity at B is 50 m/s) and \( t_i = 0\ s \), \( t_f = 25\ s \).
\( a=\frac{50 - 0}{25 - 0}=\frac{50}{25}=2\ m/s^{2} \)

Answer:

2 m/s² (corresponding to the orange option: 2 m/s²)