How Do You Calculate Velocity Change with Time-Dependent Acceleration?

  • Thread starter Thread starter Ginerva123
  • Start date Start date
  • Tags Tags
    Acceleration Time
AI Thread Summary
To calculate the velocity of the bus at time t2 = 2.10s with a time-dependent acceleration a(t) = 1.24 m/s³, integration of the acceleration function is necessary. The initial velocity at t1 = 1.15s is given as 4.94 m/s. By integrating the acceleration function with respect to time and applying the initial conditions, the constant of integration can be determined. After finding the integrated velocity function, substituting t2 will yield the bus's velocity at that time. This method effectively addresses the challenge of non-constant acceleration in the problem.
Ginerva123
Messages
13
Reaction score
0

Homework Statement



The acceleration of a bus is given by , a(t) = xa where x = 1.24 m/s3 is a constant. If the bus's velocity at time t1 = 1.15s is 4.94 m/s, what is its velocity at time t2 = 2.10s ?

Homework Equations



I know I have to integrate somehow, but the only equation I can think of to apply is
v(t) = v (initial) + integral of [a dt] with boundaries t and 0.

The Attempt at a Solution



I tried using the basic equations of motion, but they all assume that acceleration is constant... then I tried the above equation but I'm having trouble finding the intial velocity. Please help!
 
Physics news on Phys.org
The value of x = 1.24m/s^3 Therefore 'a' must be time t. Integrate the function wrt. time. Using t1 and the velocity find the constant of integration. Now put t2 = 2.1s and find the velocity.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Relating acceleration to distance and time
Replies
5
Views
3K
Zero velocity for a time interval, what about acceleration?
Replies
7
Views
2K
Find the change in the time required, if acceleration increases by the differential amount 'da'
Replies
7
Views
1K
Finding the change in velocity from an acceleration vs time graph
Replies
1
Views
3K
In a constant acceleration motion, Is it possible to have constant speed?
Replies
11
Views
1K
Solving for Work Done When Accelerating a Mass
Replies
3
Views
780
Compare the ratio of two times t1/t2 in this vertical jump
Replies
3
Views
1K
An expression for the vertical velocity as a function of time
Replies
5
Views
2K
Non-constant acceleration, solving for velocity
Replies
11
Views
2K
Irodov 1.23 confusion: Calculate distance traveled and time elapsed for this decelerating particle
Replies
2
Views
865

Hot Threads

Recent Insights

Back
Top