4.1 Displacement and Velocity Vectors

The position function of a particle is $\overset{\rightarrow}{r} \left(t\right) = 3.0 t^{3} \hat{i} + 4.0 \hat{j} .$ (a) What is the instantaneous velocity at t = 3 s? (b) Is the average velocity between 2 s and 4 s equal to the instantaneous velocity at t = 3 s?

What form does the trajectory of a particle have if the distance from any point A to point B is equal to the magnitude of the displacement from A to B?

If the instantaneous velocity is zero, what can be said about the slope of the position function?

The coordinates of a particle in a rectangular coordinate system are (1.0, –4.0, 6.0). What is the position vector of the particle?

The 18th hole at Pebble Beach Golf Course is a dogleg to the left of length 496.0 m. The fairway off the tee is taken to be the x direction. A golfer hits his tee shot a distance of 300.0 m, corresponding to a displacement $\Delta \overset{\rightarrow}{r}_{1} = 300.0 \text{m} \hat{i} ,$ and hits his second shot 189.0 m with a displacement $\Delta \overset{\rightarrow}{r}_{2} = 172.0 \text{m} \hat{i} + 80.3 \text{m} \hat{j} .$ What is the final displacement of the golf ball from where it started?

A cyclist rides 5.0 km due east, then 10.0 km $20 °$ west of north. From this point she rides 8.0 km due west. What is the final displacement from where the cyclist started?

The position of a particle is $\overset{\rightarrow}{r} \left(t\right) = 4.0 t^{2} \hat{i} - 3.0 \hat{j} + 2.0 t^{3} \hat{k} \text{m} .$ (a) What is the velocity of the particle at 0 s and at $1.0$ s? (b) What is the average velocity between 0 s and $1.0$ s?

The F-35B Lighting II is a short-takeoff and vertical landing fighter jet. If it does a vertical takeoff to 20.00-m height above the ground and then follows a flight path angled at $30 °$ with respect to the ground for 20.00 km, what is the final displacement?