Classify \(9\) kg, \(9\) N east, and \(9\) m as scalars or vectors.

A temperature changes from \(12^\circ\)C to \(19^\circ\)C. Calculate the scalar change.

A cyclist travels \(3\) km east then \(4\) km north. Find the total distance travelled and explain why it is scalar.

A force has magnitude \(15\) N and points west. Identify the scalar part and the vector information.

A lift rises from height \(2\) m to \(17\) m. Find the scalar height change and the upward displacement vector.

A runner completes one \(400\) m lap and finishes where she started. Find distance travelled and displacement.

A box has mass \(8\) kg and weight \(78.4\) N downward. Identify the scalar and vector quantities.

A speedometer reads \(22\) m s\(^{-1}\), while velocity is \(22\) m s\(^{-1}\) south. Explain the mathematical difference.

A block moves along a line from \(x=-3\) m to \(x=5\) m. Find the scalar distance between the positions.

A vector velocity is \((-6,8)\) m s\(^{-1}\). Find the scalar speed.

A parcel is displaced by \((2,-1,2)\) m under a force of magnitude \(5\) N. Which given quantity is scalar and which is vector?

A scalar \(k=-3\) multiplies \(\mathbf v=(2,-5)\). Calculate \(k\mathbf v\) and describe the direction change.

A car travels \(50\) km north then \(50\) km south. Find scalar distance and vector displacement.

A displacement vector is \(\mathbf d=(5,12)\) m. Find the scalar distance from start to finish.

A plane has ground velocity \(\mathbf v=(120,50)\) km h\(^{-1}\). Find the scalar speed.

An object has kinetic energy \(32\) J and momentum \(\mathbf p=(6,8,0)\) kg m s\(^{-1}\). Identify each type and find \(|\mathbf p|\).

A one-dimensional velocity is \(-4\) m s\(^{-1}\). Find the scalar speed and the direction information.

A force \(\mathbf F=(6,2)\) N moves an object by \(\mathbf s=(3,0)\) m, giving \(W=18\) J. Calculate the work and explain why the answer is scalar even though the inputs are vectors.

A vector velocity \(\mathbf v=(a,4)\) m s\(^{-1}\) has scalar speed \(5\) m s\(^{-1}\). Find possible values of \(a\), then state the two possible directions qualitatively.

A hiker walks \(2\) km east, \(2\) km north, \(2\) km west, and \(2\) km south, taking \(2\) hours in total. Find scalar distance, displacement, average speed, and average velocity.