Solving Rectilinear Problems - Example Problem 2.2-2

 

A particle travels along a straight line with a velocity given by v = (3 + 12t –3t ²) m/s. When t = 1 s, the particle is located 50 m to the left of the origin. Determine the acceleration when t = 4 s, the displacement from t = 0 to t = 10 s, and the total distance the particle travels during this time period.

 

Given:

• v = (3 + 12t –3t ²) m/s
• s = -50 m @ t₁ = 1 s
• t₀ = 0
• t₄ = 4 s
• t₁₀ = 10 s

 

Find:

• a @ t₄
• Δs between t₀ and t₁₀
• s_total between t₀ and t₁₀

 

Solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Remember that the givens and finds give us a clue as to which equations we need to use.

 

If velocity is a function of time and we need to find acceleration, which equation should we use?

 

v = ds/dt
a = dv/dt
a ds = v dv