A particle's velocity is given by $\stackrel{\rightharpoonup }{v}=\left(3t\frac{m}{s}\right)\widehat{i}+\left(4t^3\frac{m}{s}\right)\widehat{j}$. What are the x and y components of its acceleration at $t=2\mathrm{s}$?

(II) On mountainous downhill roads, an escape lane is sometimes placed to the side of the road for trucks whose brakes might fail. Assuming a constant upward slope of 26°, calculate the horizontal and vertical components of the acceleration of a truck that slowed from 110 km/h to rest in 7.0 s. See Fig. 3–43.

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(I) A diver running 2.5 m/s dives out horizontally from the edge of a vertical cliff and 3.5 s later reaches the water below. How high was the cliff and how far from its base did the diver hit the water?

(II) A ball thrown horizontally at 10.8 m/s from the roof of a building lands 21.0 m from the base of the building. How high is the building?

A football at rest is kicked by a football kicker. The ball is in contact with the kicker's foot for 0.050s, during which it experiences an acceleration a = 340 m/s². The ball is launched at an angle of 40° above the ground (x-axis). Calculate the horizontal and vertical components of the launch velocity.

(II) A car is moving with speed 16.0 m/s due south at one moment and 25.7 m/s due east 8.00 s later. Over this time interval, determine the magnitude and direction of (a) its average velocity, (b) its average acceleration. (c) What is its average speed? [Hint: Can you determine all these from the information given?]