The position of a particle moving along x axis is given in cm by , where t is in seconds. Calculate (a) the average velocity during time interval t=2 s to t=3 s; (b) the instantaneous velocity at t=2 s; (c) the instantaneous velocity at t=3s; (d) the instantaneous velocity at t=2.5 s; (e) the instantaneous velocity when the particle is midway between its positions at t=2 s and t=3 s (f) Graph x vs. t and indicate your answers graphically.
(a) The average velocity during t=2.00 s to t=3.00 s is 28.5 cm/s.
(b) Instantaneous velocity at t=2.00 s is 18.0 cm/s
(c) Instantaneous velocity at t=3.00 is 40.5 cm/s.
(d) Instantaneous velocity at t=2.50 s is 28.1 cm/s.
(e) Instantaneous velocity when particle is midway between t=2.00s to is 30.3 cm/s.
The problem deals with the average velocity which is the displacement over the time. Also, it involves the instantaneous velocity of an object. It is the limit of an average velocity as the elapsed time approaches zero. Using a standard equation the average velocity in terms of displacement and time can be found. Further, instantaneous velocity can be found by taking derivative of equation of position.
It is given that,
By plugging the values of t in the above equation we get,
Using equation (i) the average velocity is,
Average velocity is 28.5 cm/s
Using equation (ii) the instantaneous velocity is
Instantaneous velocity at t=3.00 s,
Instantaneous velocity at t=2.50 s
Trying to find time of particle at midway between and , we get,
Time at midway is 2.596 s
Thus, instantaneous speed at this time
Straight line slope between t=2s to 3s gives answer of part (a) and slope of tangent at the required points would give the answers of (b), (c), (d), (e)
Suppose that a passenger intent on lunch during his first ride in a hot-air balloon accidently drops an apple over the side during the balloon’s liftoff. At the moment of the apple’s release, the balloon is accelerating upward with a magnitude of and has an upward velocity of 2 m / s magnitude . What are the (a) magnitude and (b) direction of the acceleration of the apple just after it is released? (c) Just then, is the apple moving upward or downward, or is it stationery? (d) What is the magnitude of its velocity just then? (e) In the next few moments, does the speed of the apple increase, decrease, or remain constant?
You are arguing over a cell phone while trailing an unmarked police car by ; both your car and the police car are traveling at .Your argument diverts your attention from the police car for , (long enough for you to look at the phone and yell, “I won’t do that!”). At the beginning of that ,the police officer begins braking suddenly at (a)What is the separation between the two cars when your attention finally returns? Suppose that you take another to realize your danger and begin braking. (b)If you too brake at ,what is your speed when you hit the police car?
You are to drive 300km to an interview. The interview is at 11.15 AM. You plan to drive at 100 km/h , so you leave at 8 AM, to allow some extra time. You drive at that speed for the first 100 km, but then construction work forces you to slow to 40 km/h for 40km. What would be the least speed needed for the rest of the trip to arrive in time for the interview?
94% of StudySmarter users get better grades.Sign up for free