A car's velocity as a function of time is given by vz (t) = a + bt², where a = 3.0 m/s and b = 2.0 m/s³. a) Calculate the average acceleration for the interval t= 0 to t= 5.0 s. b) Calculate the instantaneous acceleration at t = 0 andt=5.0 s.
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- 2.68 0. CALC An object's velocity is measured to be v,(1) = a – Bt², . 4.00 m/s and B = 2.00 m/s. At t = 0 the object is at x = 0. (a) Calculate the object's position and acceleration as functions of time. (b) What is the object's maximum positive displacement from the origin? where a =Cheetahs can accelerate to a speed of 20.2 m/s in 2.65 s and can continue to accelerate to reach a top speed of 29.0 m/s . Assume the acceleration is constant until the top speed is reached and is zero thereafter. Let the +? direction point in the direction the cheetah runs.Express the cheetah's top speed ?top in miles per hour (mi/h) .Starting from a crouched position, how much time ?accel does it take a cheetah to reach its top speed and what distance ? does it travel in that time?In m/s?, what is the acceleration when t = 7.5 sec? Express your answer as an integer, not as a fraction. 20 15 10 10 15 25 t(sec) -5 -10 -15 -20 v(m/sec) 20
- a car is traveling at the speed Vo on a straight, level road. After the brakes are applied at t=0, the motion can be approximatd by x=t^3/100-t^2+17t where x is the distance traveled in meters and t is the time in seconds. What is the max acceleration during brake?Driving along a crowded freeway, you notice that it takes atime t to go from one mile marker to the next. When you increaseyour speed by 7.9 mi>h, the time to go one mile decreases by 13 s.What was your original speed?An object moves along the x axis according to the equation x = 3.55t2 - 2.00t + 3.00, where x is in meters andt is in seconds. (a) Determine the average speed betweent = 1.80 s and t = 2.90 s. m/s (b) Determine the instantaneous speed at t = 1.80 s. m/s Determine the instantaneous speed at t = 2.90 s. m/s (c) Determine the average acceleration between t = 1.80 s and t = 2.90 s. m/s2 (d) Determine the instantaneous acceleration at t = 1.80 s. m/s2 Determine the instantaneous acceleration at t = 2.90 s. m/s? (e) At what time is the object at rest?
- Some experimental researcher tells us that the position of an object as a function of time is given by x(t) = at3 - bt2 + ct - d, where the constants are a = 3.6 m/s3, b = 4.0 m/s2, c = 60 m/s and d = 7.0 m. Find the average acceleration over the first 2.4 seconds. A) 18 m/s/s B) 54 m/s/s C)36 m/s/s D) 76 m/s/sA body moving in a straight line. The following equation determines its location (3-x=2+t(t), noting that The location is measured in meters and the time is measured in seconds . Find out the times when there is a site The object is at point zero, i.e. 0 = x t=0 and t=1 t=1 and t=3 t=0 or t=1 t=1or t=2 t=1and t=2A rocket sled having an initial speed of 150 mi/hr is slowed by a channel of water. Assume that during the braking process, the acceleration a is given by a(v)=-mu v2 , where v is the velocity and mu is a constant. If it requires a distance of 2000 ft to slow the sled to 15 mi/hr, determine the value of mu?
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