Velocity and Acceleration Question

[mossfan563]

Homework Statement

The position of a particle moving along the x-axis depends on the time according to the equation x = c(t^5) - b(t^7), where x is in meters and t in seconds. Let c and b have numerical values 2.6 m/s5 and 1.3 m/s7, respectively. From t = 0.0 s to t = 1.8 s, (a) what is the displacement of the particle? Find its velocity at times (b) 1.0 s, (c) 2.0 s, (d) 3.0 s, and (e) 4.0 s. Find its acceleration at (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s.


2. The attempt at a solution
Do I try to take the derivative to try and get the velocity and acceleration answers?
And how do I find the displacement?

 

[LowlyPion]

Homework Statement

The position of a particle moving along the x-axis depends on the time according to the equation x = c(t^5) - b(t^7), where x is in meters and t in seconds. Let c and b have numerical values 2.6 m/s5 and 1.3 m/s7, respectively. From t = 0.0 s to t = 1.8 s, (a) what is the displacement of the particle? Find its velocity at times (b) 1.0 s, (c) 2.0 s, (d) 3.0 s, and (e) 4.0 s. Find its acceleration at (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s.2. The attempt at a solution
Do I try to take the derivative to try and get the velocity and acceleration answers?
And how do I find the displacement?

The displacement should be found by using the position function f(t) = x = c*t⁵ - b*t⁷ and then determining the difference between the two positions at the times given.

As to the rest of your question if velocity is $$\frac{dx}{dt}$$ and acceleration is $$\frac{dv}{dt}$$ then taking derivatives looks like a sound approach and then plug in the points asked for.

 

[baba89]

Yes, taking the derivative with respect to time will give you the velocity and acceleration at different times. To find the displacement, you can use the formula s=vt, where s is the displacement, v is the velocity, and t is the time. So for part (a), you can plug in the values for t=0.0 s and t=1.8 s into the equation and subtract the two to find the displacement. For parts (b)-(e), you can plug in the given values of time into the derivative of the position equation to find the velocity at those specific times. For parts (f)-(i), you can take the derivative of the velocity equation to find the acceleration at those specific times.