Mechanics displacement Question

In summary, the problem involves a drag racer starting from rest at the origin and moving along a straight line with a velocity of v = 5t^2. The expression for the displacement of the car from t = 0 to time t is given as 5t^3/3. The student attempted to solve for the displacement using the equation Vfinal-Vinitial/2)t=X but kept getting 5t^3/2. They were advised to use calculus and integrate the equation ds/dt = 5t^2 to find the correct answer of 5t^3/3.
  • #1
Kommandant
15
0

Homework Statement


At time t = 0 a drag racer starts from rest at the origin and moves along a straight line with velocity given by v = 5t^2, where v is in m/s and t in s. The expression for the displacement of the car from t = 0 to time t is
(a) 5t^3
(b) 5t^3/3
(c) 10t
(d) 15t^2
(e) 5t/2


Homework Equations


(Vfinal-Vinitial/2)t=X
Vfinal=5t^2

The Attempt at a Solution



The manual says B

But I keep Getting 5t^3/2

Vfinal=5t^2

Vinitial=0
so
(5t^2/2)t=x
5t^3/2
 
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  • #2
u have to apply integration here
 
  • #3
Oh... I am not versed in calculus at all :l. could you explain the process?
 
  • #4
express v as ds/dt. then bring the dt to other side of the equation. then integrate both sides.
 
  • #5
Alright, thanks for your help!
 

1. What is displacement in mechanics?

Displacement in mechanics refers to the distance and direction of an object's change in position from its starting point. It is a vector quantity that takes into account both magnitude and direction.

2. How is displacement different from distance?

Distance is a scalar quantity that refers to the total length traveled by an object, while displacement is a vector quantity that takes into account the object's starting and ending positions. Distance is always positive, while displacement can be either positive or negative depending on the direction of the movement.

3. How do you calculate displacement?

Displacement is calculated by subtracting the initial position from the final position. In equation form, it is represented as Δx = xf - xi, where Δx is displacement, xf is the final position, and xi is the initial position.

4. Can displacement be negative?

Yes, displacement can be negative if the object moves in the opposite direction of the chosen positive direction. For example, if an object moves 5 meters to the left from its starting position, its displacement would be -5 meters.

5. What is the SI unit of displacement?

The SI unit of displacement is meters (m). However, other units such as centimeters (cm) or kilometers (km) can also be used to measure displacement.

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