A question (1 Viewer)

[BlueGas]

I need help for this question even though it may seem easy.

i), v = 0 when t = 3

ii) Basically I should be looking for the times when f''(x) = 0, or when it's a point of inflexion, right?

But the answer says t = 1/2 and t = 2, and these are stationary points, but that's when f'(x) = 0, I need some clarifying here.

iii) Shaded area represents distance travelled in the first second

iv) The answer is apparently t = 2, but how? From what I know, a particle reaches the origin when it hits the t-axis. I also need clarifying here because I may be wrong.

 

[rand_althor]

ii) This graph (lets call it v(t)), is the velocity function. The gradient of this function represents acceleration. So to find when acceleration is zero, you find the stationary points of this graph (the velocity function), which can be found by letting v'(t)=0. v'(t) is the same as f''(x), if f(x) is the displacement function. If you were given a graph showing the displacement, then you would find f''(x)=0.

iv) That is true if the graph is a displacement-time graph. This, however, is a velocity-time graph. The distance traveled by the particle is the area under this graph. The particle will return to the origin when the total area under the graph is equal to zero. If you find the area under the graph from t=0 to t=2, the positive and negative areas cancel out, leading to a displacement of zero. Hence the particle has returned to the origin at t=2.

 

[BlueGas]

ii) This graph (lets call it v(t)), is the velocity function. The gradient of this function represents acceleration. So to find when acceleration is zero, you find the stationary points of this graph (the velocity function), which can be found by letting v'(t)=0. v'(t) is the same as f''(x), if f(x) is the displacement function. If you were given a graph showing the displacement, then you would find f''(x)=0.

iv) That is true if the graph is a displacement-time graph. This, however, is a velocity-time graph. The distance traveled by the particle is the area under this graph. The particle will return to the origin when the total area under the graph is equal to zero. If you find the area under the graph from t=0 to t=2, the positive and negative areas cancel out, leading to a displacement of zero. Hence the particle has returned to the origin at t=2.

Okay so how about an acceleration-time graph? How would I know when it reaches the origin?